Author: Ali Ovais
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659260360
Category :
Languages : en
Pages : 60
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Book Description
There are many motivational problems related to the non-pure fields extension corresponding to the algebraic numbers (1+(r) DEGREES(1/n)) DEGREES(1/m), where m and n are positive integers. Here we take the extended field K over the field of rational numbers Q of degree n correspond to the inner nth root of the algebraic number and then the relative extension of degree m is taken over field K. If we interchange these nth and mth root then the whole structure and the resulting Hasse diagram change completely. In chapter 4 We have posed an open problem for the non-pure sextic field whose Galois closure is of extension degree 36. Since there are 14 groups of order 36 out of which four are abelian and ten are non-abelian and our group of automorphism is non-abelian so it is one of the ten. We had not only found this group but also create the correspondence between the Hasse diagram of subfields of Galois closure and the subgroups of group of aut
Author: Jew-Chen John Hwang
Publisher:
ISBN:
Category : Equations, Cubic
Languages : en
Pages : 212
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Book Description
Author: Michael William Mastropietro
Publisher:
ISBN:
Category :
Languages : en
Pages : 164
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Book Description
Author: Jacqueline Palermo
Publisher:
ISBN:
Category : Equations, Quadratic
Languages : en
Pages : 42
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Book Description
Author: István Gaál
Publisher: Springer Nature
ISBN: 3030238652
Category : Mathematics
Languages : en
Pages : 326
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Book Description
Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.
Author: Jew-Chen (John). Hwang
Publisher:
ISBN:
Category : Equations, Cubic
Languages : fr
Pages : 106
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Book Description
Author: Richard A. Mollin
Publisher: CRC Press
ISBN: 9780849339899
Category : Mathematics
Languages : en
Pages : 504
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Book Description
From its history as an elegant but abstract area of mathematics, algebraic number theory now takes its place as a useful and accessible study with important real-world practicality. Unique among algebraic number theory texts, this important work offers a wealth of applications to cryptography, including factoring, primality-testing, and public-key cryptosystems. A follow-up to Dr. Mollin's popular Fundamental Number Theory with Applications, Algebraic Number Theory provides a global approach to the subject that selectively avoids local theory. Instead, it carefully leads the student through each topic from the level of the algebraic integer, to the arithmetic of number fields, to ideal theory, and closes with reciprocity laws. In each chapter the author includes a section on a cryptographic application of the ideas presented, effectively demonstrating the pragmatic side of theory. In this way Algebraic Number Theory provides a comprehensible yet thorough treatment of the material. Written for upper-level undergraduate and graduate courses in algebraic number theory, this one-of-a-kind text brings the subject matter to life with historical background and real-world practicality. It easily serves as the basis for a range of courses, from bare-bones algebraic number theory, to a course rich with cryptography applications, to a course using the basic theory to prove Fermat's Last Theorem for regular primes. Its offering of over 430 exercises with odd-numbered solutions provided in the back of the book and, even-numbered solutions available a separate manual makes this the ideal text for both students and instructors.
Author: Henri Cohen
Publisher: Springer Science & Business Media
ISBN: 1441984895
Category : Mathematics
Languages : en
Pages : 591
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Book Description
Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.
Author:
Publisher:
ISBN:
Category : Number theory
Languages : en
Pages : 804
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Book Description
Author: Daniel A. Marcus
Publisher: Springer
ISBN: 3319902334
Category : Mathematics
Languages : en
Pages : 213
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Book Description
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.
